1. The vertex of a parabola is at $(12, -4)$, and its axis of symmetry is vertical. One of the $x$-intercepts is at $(15, 0)$. What is the $x$-coordinate of the other $x$-intercept?
2. The $x$-intercepts of the parabola $y = x^2 + bx + c$ are $(-3,0)$ and $(5,0).$ Find the equation of the parabola, and submit your answer in $y = ax^2 + bx + c$ form.